The purpose of a timepiece escapement system is to maintain and to count the oscillations of the balance wheel of a sprung balance resonator. To achieve this, the system receives the energy provided by a barrel and at the end of the chain by a seconds wheel in order to periodically allow a fragment of this drive energy to escape in order to give to the resonator energy lost through passive resistance (for example friction), the resonator including an inertia fly-wheel called a balance on the staff of which there is fixed a spiral spring called a balance spring.
The mechanical energy Em of this type of sprung balance resonator is given by the following relation:
                              E          m                =                                            1              2                        ⁢                          kA              2                                =                                    1              2                        ⁢                                          J                ⁡                                  (                                      2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                    f                                    )                                            2                        ⁢                          A              2                                                          (        1        )            where:                J is the inertia of the balance;        f is the frequency of the balance;        A is the oscillation amplitude of the balance.        
Watchmaking technology tends to increase the energy of the sprung balance resonator in order to improve its precision and shock resistance, owing to the increase in the inertia J of the balance and/or the increase in the oscillation frequency f of the balance. However the increase in these parameters causes great difficulties.
Indeed, the increase in the inertia J of the balance tends to increase its weight which causes unwanted dry friction and/or lowers its aerodynamics. Further, the increase in oscillation frequency f requires a considerable increase in virtual power which is liable to decrease the power reserve of the timepiece. It is also clear that the increase in oscillation frequency f necessarily means that the escapement functions become shorter and shorter which represents a real kinematic and tribological challenge.